User:LouHoe/sandbox

Louis Hoelbling has developed these figures he calls Geometric Magic Meshes. There are countless geometric Magic Meshes, either similar to Magic squares, where each row has identical number of cells throughout the figure, or similar to Magic Hexagons, where the number of cells in each row increase by one when inspecting the parallel rows from an edge of the figure.

Geometric Magic Meshes are characterized into two different orders. They are order two and order 3. Order 2 are those Magic Meshes where a cell generally exists in at least two different rows. Similarly, Order 3 Magic Meshes have cells that exist in at least 3 different rows. Magic Squares are a well known order 2 magic mesh, and magical hexagons are well known order 3 magic mesh.

Here are two examples of 3 sided Magic Meshes: The above is what I call an order 2 three sided magic mesh that has 5 cells per external side, and it uses the numbers 0 to 18 once and only once where each row adds to 49. The right picture illustrates how the rows flow in the figure. The figure has 3 diagonals indicated by the blue path, and a total of 6 other paths parallel to the three sides of the figure, indicated by the two red lines. Each row has the identical number of cells, ie... 5 cells per row, similar to the construction of standard Magic Squares. And just like magic Squares, you can add a constant value to each and every cell and you will still be magic, where the sum of all rows would be 49+5n, and the numbers used would be 0+n to 18+n, used once and only once.